To simplify the expression \((-x^2 - 3x + 5) - (6x^2 - 1)\), we will first distribute the negative sign across the second parenthesis:
\[ (-x^2 - 3x + 5) - (6x^2 - 1) = -x^2 - 3x + 5 - 6x^2 + 1 \]
Next, we combine like terms. We will combine the \(x^2\) terms, the \(x\) terms, and the constant terms separately:
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Combine \(x^2\) terms: \(-x^2 - 6x^2 = -7x^2\)
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Combine \(x\) terms: \(-3x\)
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Combine constant terms: \(5 + 1 = 6\)
Putting it all together, we have:
\[ -7x^2 - 3x + 6 \]
Thus, the simplified expression is:
\[ \boxed{-7x^2 - 3x + 6} \]
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